Draw a line l and take a point P outside it.Through p,draw a line M parallel to L.Mark another point Q on M and draw the perpendicular bisector of PQ intersecting line L at R.Join PR and QR.Name the triangle formed.

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$$\begin{gathered} \mathrm{Follow} \mathrm{the} \mathrm{following} \mathrm{steps} \mathrm{of} \mathrm{construction}. \\ 1. \mathrm{Draw} \mathrm{a} \mathrm{line} \mathrm{l} \mathrm{and} \mathrm{take} \mathrm{any} \mathrm{point} \mathrm{P} \mathrm{outside} \mathrm{this} \mathrm{line}. \\ 2. \mathrm{Take} \mathrm{any} \mathrm{arbitraray} \mathrm{point} \mathrm{S} \mathrm{on} \mathrm{line} \mathrm{l} \mathrm{and} \mathrm{join} \mathrm{P} \mathrm{with} \mathrm{S} \\ 3. \mathrm{To} \mathrm{draw} \mathrm{a} \mathrm{line} \mathrm{through} \mathrm{P} \mathrm{parallel} \mathrm{to} \mathrm{line} \mathrm{l}, \mathrm{make} \mathrm{an} \mathrm{angle} \mathrm{at} \mathrm{P} \mathrm{equal} \mathrm{to} \\ \mathrm{angle} \mathrm{at} \mathrm{S} \mathrm{so} \mathrm{that} \mathrm{laternate} \mathrm{pair} \mathrm{of} \mathrm{angles} \mathrm{are} \mathrm{equal}. \mathrm{Extend} \mathrm{it} \mathrm{to} \mathrm{get} \mathrm{line} \mathrm{M} \\ 4. \mathrm{Take} \mathrm{any} \mathrm{point} \mathrm{Q} \mathrm{on} \mathrm{line} \mathrm{M}. \\ 5. \mathrm{To} \mathrm{daw} \mathrm{perpendicular} \mathrm{bisector} \mathrm{of} \mathrm{PQ}, \mathrm{take} \mathrm{P} \mathrm{as} \mathrm{center} \mathrm{and} \mathrm{radius} \mathrm{more} \mathrm{than} \\ \mathrm{half} \mathrm{of} \mathrm{PQ}, \mathrm{draw} \mathrm{an} \mathrm{arc} \mathrm{above} \mathrm{and} \mathrm{below} \mathrm{the} \mathrm{line} \mathrm{PQ} \\ 6. \mathrm{Again} \mathrm{with} \mathrm{Q} \mathrm{as} \mathrm{center} \mathrm{and} \mathrm{with} \mathrm{same}, \mathrm{draw} \mathrm{another} \mathrm{arc} \mathrm{whcih} \mathrm{intersects} \mathrm{the} \mathrm{first} \mathrm{arc} \\ 7. \mathrm{Join} \mathrm{these} \mathrm{points} \mathrm{of} \mathrm{intersection} \mathrm{of} \mathrm{arcs} \mathrm{which} \mathrm{intersects} \mathrm{the} \mathrm{line} \mathrm{l} \mathrm{at} \mathrm{poinr} \mathrm{R}. \\ 8. \mathrm{Join} \mathrm{PR} \mathrm{and} \mathrm{QR} \mathrm{to} \mathrm{get} △\mathrm{PQR} \\ \mathbf{Then}\mathbf{ }\mathbf{△}\mathbf{PQR}\mathbf{ }\mathbf{is}\mathbf{ }\mathbf{an}\mathbf{ }\mathbf{isoscleles}\mathbf{ }\mathbf{triangle}\mathbf{ }\mathbf{with}\mathbf{ }\mathbf{PR}\mathbf{=}\mathbf{QR} \end{gathered}$$





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